The present invention relates to shelf brackets of the type which are adapted for mounting at the rear end thereof on an upright supporting surface to extend in generally cantilever fashion from the supporting surface. It is common practice to make shelf brackets of this type with an all metal construction in which the shelf brackets have integral lugs or hooks at the rear ends for engaging in openings in upright mounting standards. However, it is sometimes desirable to make the shelf brackets of a non-metallic material such as wood, wood particle board or plastic. In order to mount such shelf brackets of non-metallic material, it has heretofore been proposed, for example as shown in U.S. Pat. Nos. 3,190,243; 3,265,344 and 3,295,474 to provide a metal attaching member at the rear of the shelf brackets and to secure the metal attaching member to the shelf brackets as by screws that extend horizontally into the ends of the shelf brackets. When a downward load is applied to the shelf brackets, the bracket tends to fulcrum about its lower rear edge and the upper portion of the bracket tends to pull away from the supporting surface and withdraw the screws out of the shelf bracket. The holding power of screws in many non-metallic materials, for example in the end grain of many woods, wood particle board, and many plastics is not sufficiently high that it can be safely relied upon to withstand such withdrawal forces. It has also been proposed, as shown in U.S. Pat. No. 3,432,134, to provide a U-shaped metal attaching member for mounting the non-metallic shelf bracket on a support surface with the U-shaped attaching member overlapping opposite sides of the shelf bracket and with the fasteners extending crosswise of the bracket. Such a metal attaching member is more complex and expensive to manufacture and, moreover, is exposed at the sides of the shelf bracket and consequently adversely affects the aesthetic appearance of the shelf bracket. It has also been been proposed, as shown in U.S. Pat. No. 3,672,624, to attach a non-metallic shelf bracket to a support using a metal hook that extends into a downwardly and rearwardly inclined opening in the top of the shelf bracket. With this arrangement, the downwardly and rearwardly extending hook must take both of horizontal separating forces between the bracket member and the support as well as the vertical load on the bracket member. Moreover, because of the manner in which the metal attaching member is mounted on the shelf bracket, the metal attaching member must have its wall mounting portion disposed above the top of the shelf bracket, as shown in that patent.